Abstract

Consider a periodic system of N point ions of charge Ze and mass M in a rigid, neutralizing uniform background. For a given configuration \(\mathop r\limits^{ \to N} = \left( {{{\mathop r\limits^ \to }_1},\mathop {{r_2}}\limits^ \to ...,{{\mathop r\limits^ \to }_{\rm N}}} \right)\) of the ions, the total potential energy of the system is:

Excess thermodynamic properties, and more generally, all reduced(dimensionless) equilibrium properties depend on the single dimensionless variable:

$$\Gamma = {\frac{{\left( {Ze} \right)}}{{a{k_B}T}}^2}$$

(1.3)

where a = (3/4πρ)1/3, ρ = N/V. We shall frequently use reduced distance x = r/a and wave numbers q = k/a. To describe dynamical (or time-dependent) properties we introduce an additional time variable t which we express in a “natural” unit, equal to the inverse of the plasma frequency: